Estimating maximal symmetries of regression functions via subgroup lattices
成果类型：
Article; Early Access
署名作者：
Christie, Louis G.; Aston, John A. D.
署名单位：
University of Cambridge
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1093/jrsssb/qkaf031
发表日期：
2025
关键词：
摘要：
We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries. Symmetry estimation is carried out using hypothesis testing for invariance strategically over the subgroup lattice of a search group G acting on the feature space. We show that the estimation of the unique largest invariant subgroup of G generalizes useful tools from linear dimension reduction to a non-linear context. We show that the estimation is consistent when the subgroup lattice chosen is finite, even when some of the subgroups themselves are infinite. We demonstrate the performance of this estimator in synthetic settings and apply the methods to 2 data sets: satellite measurements of the Earth's magnetic field intensity and the distribution of sunspots.
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